Extremal behavior of large cells in the Poisson hyperplane mosaic

DOI10.1214/23-ejp1049zbMath1528.60049arXiv2106.14823OpenAlexW3174031767MaRDI QIDQ6136815

Moritz Otto

Publication date: 17 January 2024

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.14823

zbMATH Keywords

Palm distributionChen-Stein methodrandom mosaicBlaschke-Petkantschin formulaPoisson hyperplane processKantorovich-Rubinstein metricpoint process approximationKendall's problemmaximum cell

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

• Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry
• Asymptotic shapes of large cells in random tessellations
• Central limit theorems for Poisson hyperplane tessellations
• Stein's method and point process approximation
• The limit shape of the zero cell in a stationary Poisson hyperplane tessellation.
• Gaussian limits for random geometric measures
• Typical cells in Poisson hyperplane tessellations
• Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space?
• Poisson process approximation under stabilization and Palm coupling
• A Remark on Stirling's Formula
• Stochastic and Integral Geometry
• Lectures on the Poisson Process
• Extremes for the inradius in the Poisson line tessellation
• Large nearest neighbour balls in hyperbolic stochastic geometry
• Unnamed Item

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